RCL 40 Book On Sale

RCL 40 Book On Sale

The fantastic book, RCL 40: Recollection, Reinvention, & HP Calculators, edited by W.A.C. Mier-Jedrezejowic, Ph. D, Mark Power, and Bruce Horrocks is a collection of articles from mathematicians, programmers, and calculator enthusiasts.  This books covers the legendary HP 41C, the Swiss Micros equivalent, the DM41 family, to engineers' experiences working for Hewlett Packard.   I wrote a chapter in the book where I talk about my experiences with the HP 41C and DM41X.   

RCL 40 is a celebration of the HP 41C and calculators.   

To order, please click here.  The book is published by the HPCC in the United Kingdom.  

Eddie 

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Casio fx-9750GIII: Effects of Rounding

 Casio fx-9750GIII:  Effects of Rounding

How Accurate?

The program ROUNDS compare true results against the true results in one of five calculations:

1.  A × B × C

2.  A × B ÷ C

3.  √(A^2 + B^2 - C^2)

4.  A ÷ B ÷ C

5.  (A + 1 ÷ B)^C

The rounded result is calculated after rounding after each step.

For example:  A × B × C

True result:  

T = A × B × C

Rounded Result:

R = round(A × B)

R = round(R × C)

The absolute error percentage is calculated.   

Casio fx-9750GIII Program:  ROUNDS

"2022-11-23 EWS"

"EFFECTS OF ROUNDING"

"# OF PLACES"?→N

"A"?→A

"B"?→B

"C"?→C

Menu "SELECT OPERATION",

"A×B×C",A

"A×B÷C",B

"√(A^2 + B^2 - C^2)",C

"A÷B÷C",D

"(A+1÷B)^C",E

Lbl A

RndFix(A×B,N)→R

RndFix(R×C,N)→R

A×B×C→T

Goto 1

Lbl B

RndFix(A×B,N)→R

RndFix(R÷C,N)→R

A×B÷C→T

Goto 1

Lbl C

RndFix(A²+B²,N)→R

RndFix(√(R-C²),N)→R

√(A²+B²- C²)→T

Goto 1

Lbl D

RndFix(A÷B,N)→R

RndFix(R÷C,N)→R

A÷B÷C→T

Goto 1

Lbl E

RndFix(A+1÷B,N)→R

RndFix(R^C,N)→R

(A+1÷B)^C→T

Goto 1

Lbl 1

RndFix(100×Abs (R-T)÷T,5)→E

ClrText

Locate 1,3,"ROUNDED:"

Locate 9,3,R

Locate 1,4,"ACTUAL:"

Locate 9,4,T

Locate 1,5,"ERROR%:"

Locate 9,5

Example:

Let A = 13.946, B = 11.9765, C = π^3/4

Round to 2 decimal places (N = 2)

1.  A × B × C

Rounded:  1294.67

Actual:  1294.700174

Error:  2.33*10^-3 %

2.  A × B ÷ C

Rounded: 21.55

Actual:  21.54715585

Error:  0.0132%

3.  √(A^2 + B^2 - C^2)

Rounded: 16.67

Actual:  16.66855254

Error:  8.68*10^-3 %

4.  A ÷ B ÷ C

Rounded: 0.15

Actual: 0.1502208155

Error: 0.14699%

5.  (A + 1 ÷ B)^C

Rounded: 778927217

Actual:  778710708.2

Error:  0.0278%

Enjoy,  

Eddie 

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

TI-30 XIIS and Casio fx-115ES Plus 2nd Edition: The Percent Function

TI-30 XIIS and Casio fx-115ES Plus 2nd Edition:  The Percent Function

%:  Divide by 100

Unlike computer languages, where the % symbol usually means modulo division, the % divides the argument by 100 on calculators such as the TI-30 XIIS and Casio fx-115 ES Plus 2nd Edition.

Hence 50% returns 0.5

This may provide confusion when the following is typed:

100 + 50% 

which would returns 100.5 instead of the expected 150.   

Here is how to use the percent function to our advantage in common situations.

Adding and Subtracting Percent

x + p% and x - p%

1.  Enter x and store it in a variable, preferably A.   The variable A can be advantageous, especially the TI-30 XIIS.   Access the variable A on the TI-30 XIIS by pressing [MEMVAR] [ = ] with every few keystrokes.  

2.  Enter the following:

Add percent:  A+A×p%

Subtract percent:  A-A×p%

We can omit the multiplication sign on the TI-30 XIIS.  The multiplication sign is required on the fx-115ES Plus.

Examples:

50 + 10%:   50 → A;  A+A*10%  returns 55

50 - 10%:  50 → A;  A-A*10% returns 45

Percent Change

Key strokes:  (new - old)/old%

Example:

Find the percent change from 425 to 480:

(480-425)/425%   returns 12.94117647

Financial Calculations

For the following calculations, let i=6% and n=4  (i being the periodic interest, n being number of payments).  We can see the percent function in action.

Future Value of a Present Value:  (1+i%)^n   

(1+6%)^4 returns 1.26247696

Future Annuity Value Factor:  ((1+i%)^n-1)/i%

((1+6%)^4-1)/6% returns 4.374616

Present Annuity Value Factor:  (1-(1+i%)^-n)/i%

(1-(1+6%)^-4)/6% returns 3.465105613

Hope this helps, so we can find additional calculations where this percent function can help with calculations with the TI 30 XIIS and Casio fx-115 ES Plus 2nd Edition.  

Eddie 

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Casio fx-9750GIII: Spin the Wheel

Casio fx-9750GIII:   Spin the Wheel

Making the Wheel and String Commands

The wheel is comprised of a long string.  Each space has an equal amount of characters, in this case I picked 5.  To make the wheel "spin", I use the StrRotate.

StrRotate(Str n, s):

Str n:  n from 1 to 20

s:  number of spaces to rotate the string.  If s>0 the string rotates left.  If s<0, the string rotates right.   The characters wrap around.  

If Str1 = "TESTBOOKADAM"

StrRotate(Str 1,4) returns "BOOKADAMTEST"

StrRotate(Str 1,-4) returns "ADAMTESTBOOK"

Other commands used:

StrLeft(Str n, s):   takes the left s characters of Str n

StrRight(Str n, s):  takes the right s characters of Str n

StrMid(Str n, p, m):  extracts the string starting at position n at m characters

The wheel used in this program:

BROKE  (it's bankrupt said in five characters)

$ 650

$ 550

$ 900

$ 800

$ 700

PRIZE  (prize space)

$1000

$ 600

$ 750

$ 500

$5000

5 characters per space is used.  

Casio fx-9750GIII Program:  SPIN

"2022-11-23 EWS"

"BROKE$ 650$ 550$ 900$ 800$ 700PRIZE$1000$ 600$ 750$ 500$5000"→Str 1

Lbl 1

RanInt#(20,48)→N

For 1→I To N

StrRotate(Str 1,5)→Str 1

StrLeft(Str 1,5)→Str 2

ClrText

Locate 10,3,"↓"

Locate 2,4,StrRight(Str 1,5)

Locate 8,4,Str 2

Locate 14,4,StrMid(Str 1,6,5)

Next

1DispsMenu "SPIN AGAIN?","YES",1,"NO",0

Lbl 0

ClrText

Locate 4,4,"THANK YOU"

↓ and $ are found in the CHAR menu.  

Have fun,

Eddie 

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Retro Review: Hewlett Packard HP 14B 50th Anniversary Edition

Retro Review:  Hewlett Packard HP 14B 50th Anniversary Edition

Quick Facts

Model:  HP 14B 50th Anniversary Edition 

Company:  Hewlett Packard

Years:  1989 (and probably 1990)

Type:  Finance

Batteries: 3 x LR44, SR44, AR76

Display:  1 line, alpha-numeric, 12 characters

Original Price:  $50, originally available only to Hewlett Packard's shareholders and employees 

Operating System:  Chain 

Features

*  Time Value of Money with Amortization.  Like all the HP financial calculators, the compute key is not used to calculate values.   The interest register is based on annual interest, while payments per year (P/YR) is a setting.  Beginning and ending of period payment modes are present.  

*  Cash Flows:  NPV and IRR.  These worksheets store the cash flow and make use the COMPUTE function to calculate NPV and IRR.  NPV is stored in PV while IRR is stored in I%YR.  

*  Solvers:  Cost/Price/Margin, Old/New/% Change, Nominal Rate vs. Effective 

Rate, Total/Part/% of the Total

*  Schedules:  ROI% (return on investment), Breakeven, and Inventory with Turnover analysis.   The schedules will make use of the down arrow key [ ↓ ], up arrow [ shift ] ( ↑ ), and the COMPUTE function [ shift ] (COMPUTE).  

*  Statistics:  One variable and two-variable.  Regressions included are:  

Linear:  y = m * x + b

Exponential:  y = b * e^(m * x)

Logarithmic:  y = b + m * ln x

Power:  y = b * x^m

There is also a Best fit mode, which decides the regression model based on the best correlation between the four modes.   

There are also two prediction sets  Going through the STAT menu, you can predict x and y values based on the chosen model.  Going through the FRCST (forecast) menu, the regression used is determined by the regression with the best correlation.

The Math menu contains three functions:  e^x, ln, and n!  (factorials for positive integers only).  

The 14B operates in chain mode, meaning no order of operations is followed.  The 14B operates similar to a four-function calculator in this regard.  

I think the 14B is set to be an intermediate finance calculator between the 10B and the 17B, which the 17B allows for user equations.  

The display will not only give just numbers but will also label the variables, which I always find useful.   

Golden Anniversary

The HP 14B 50th Anniversary Edition has a gold circle with a 50 logo on the top right side of the calculator.  Also on the engravement is the years 1939 - 1989.  On the leather holder, there is also the 50/1939 - 1989 logo engraved into the leather case.   

The HP 14B 50th Anniversary edition is the same of the "normal" HP 14B calculator in terms of features and excellent keyboard.

The HP 14B is part of Hewlett Packard's pioneer series, which the series includes the HP 20S, 21S, 22S, 27S, 42S, 17B, 17BII, 10B, 32S, 32SII, and 32S 50th Anniversary Edition.  It is my favorite series of Hewlett Packard calculators, both in terms of the features the calculators have and the high quality keyboards the calculators have.

50th edition calculators are available through online auction sites such as eBay for a reasonable price.  Perhaps I may add a 32S 50th Anniversary Edition to my collection.  

 

Sources:

"HP 14-B 50th Anniversary Limited Edition"   Museum of HP Calculators

https://www.hpmuseum.org/hp14b50.htm   Retrieved January 11, 2023

HP 14B Business Calculator Owner's Manual.  Hewlett Packard 

October 1988.  Download the English version here:  https://literature.hpcalc.org/items/574

Eddie

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Swiss Micros DM41X: Infinite Integrals by Gaussian Quadrature

Swiss Micros DM41X:   Infinite Integrals by Gaussian Quadrature

Introduction

The program INFGAUS calculates the integral:

∫ e^-x * f(x) dx from x = a to x = ∞

f(x) is the subroutine FX.   The subroutine starts with the x value on the stack and ends with the RTN command.

The HP 45 algorithm, which is incorporated into the program INFGAUS estimates the integral by the sum

e^-a * Σ(( w_i * f(z_i + a)) for i=1 to 3)

where 

w_1 = 0.71109390099

z_1 = 0.4157745568

w_2 = 0.2785177336

z_2 = 2.29428036

w_3 = 0.0103892565

z_3 = 6.289945083

DM41X Program:  INFGAUS

The code can work is for the entire HP 41C/DM41 family.  The calculator is set to Fix 2 mode.  Registers 01 through 08 are needed.  

01  LBL^T INFGAUS

02  .4157745568

03  STO 01

04  2.29428036

05  STO 02

06  6.289945083

07  STO 03

08  .7110930099

09  STO 04

10  .278517736

11  STO 05

12  .0103892565

13  STO 06

14  FIX 2

15  ^T A?

16  PROMPT

17  STO 07

18  RCL 01

19  +

20  XEQ^T FX

21  RCL 04

22  *

23  STO 08

24  RCL 07

25  RCL 02

26  +

27  XEQ^T FX

28  RCL 05

29  *

30  ST+ 08

31  RCL 03

32  RCL 07

33  +

34  XEQ^T FX

35  RCL 06

36  *

37  RCL 08

38  +

39  RCL 07

40  CHS

41  E↑X

42  *

43  STO 08

44  END

Examples

Example 1

∫ e^-x * x^3.99 dx from x = 0 to ∞   (calculate Γ(4.99))

LBL^T FX

3.99

Y↑X

RTN

A? 0

Result:  23.64

Example 2

∫ e^-x * x^2 ÷ (x - 1)  dx from x = 2 to ∞   

LBL^T FX

X↑2

LASTx

1

-

/

RTN

A?  2

Result:  0.62

Example 3

∫ (e^-x)^2 dx from x = 0 to ∞   

= ∫ (e^-x) * (e^-x) dx from x = 0 to ∞   

LBL^T FX

CHS

E↑X

RTN

A?  0

Result:  0.50  (it turns out 0.5 is the exact answer)

Source

HP-45 Applications Handbook  Hewlett Packard Company.  1974.

Remember, my regular posting schedule for January and February 2023 is on Saturdays only. 

Eddie 

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Casio fx-9750GIII: Decimal Expansion of a Fraction

Casio fx-9750GIII:  Decimal Expansion of a Fraction

Introduction - Happy New Year!

The program DEC21 finds a decimal expansion of a positive fraction.  This program is based on Barry Kissane's DECIMAL program from "Programming Your Calculator: Casio fx-7400G Plus" (see source below).  

Casio fx-9750GIII Program:  DEC21

244 bytes

"2022-11-22 EWS"

"FRACTION EXPANSION"

"NUM.(>0) "?→N

"DEN.(>0) "?→X

Int log (N/X)+1→T

ClrText

Locate 1,2,N

Locate 13,2,"÷"

Locate 1,3,X

Locate 13,3,"≈"

For 1→I To 21

If T=0

Then 

Locate I,5,"."

I+1→I

IfEnd

Int (N÷X)→D

10*(N-D×X)→N

Locate I,5,D

T-1→T

Next

Locate 18,1,"   "

Note:  the approximate symbol, ≈, is found in the CHAR menu.

Examples:

Example 1:

558/127

NUM:  558

DEN:  127

Result:

558 ÷

127 ≈

4.3937007874015748031

Example 2:

5/27

NUM: 5

DEN: 27

5  ÷

27  ≈

0.1851851851851851851

Here's to a great 2023!

Source

Kissane, Barry.  Programming Your Calculator: Casio fx-7400G Plus. Chatswood NSW, Australia, 2000. ISBN 0 9758302 0 3.   

Eddie

Remember, my regular posting schedule for January and February 2023 is on Saturdays only. 

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP Prime: Free Fall with Air Friction

HP Prime:   Free Fall with Air Friction 

Introduction

The program FALLS will calculate the position and velocity of an object falling with friction proportional to square of the object's speed.   The program is aimed towards large objects in free fall.  The half-increment method is used.

With the initial conditions:

y = 0  (initial position, assumed to be at zero)

g = gravitational constant

α = f/m  (force-mass ratio)

dy/dt = 0 (velocity, assume to be at rest from the beginning)

With Δt with the change of time:

dy/dt_1/2 = dy/dt_0 + C * Δt/2  where C = g - α * (dy/dt_0)^2

dy/dt_(i+1/2) = dy/dt_(i-1/2) + C * Δt where C =   g - α * (dy/dt_(i-1/2))^2

y_i+1 = y_i + dy/dt_(i+1/2) * Δt

HP Prime Program: FALLS

EXPORT FALLS()

BEGIN

// EWS 2022-11-03

HFormat:=1;

HDigits:=4; 

LOCAL t,g,a,n;

LOCAL i,d,c,y,m;

LOCAL l0,l1,l2;

LOCAL l3,l4,m0;

 

INPUT({t,g,a,n},"Fall-Air Resistance",

{"Δt =","g =","α =","n ="},

{"charge in time","gravity",

"force/mass","number of steps"});

l0:={m};

l1:={d};

l2:={y};

// for section here

FOR i FROM 1 TO n DO

c:=g-a*d^2;

IF t==0 THEN

c:=c/2;

END;

d:=d+c*t;

m:=m+t;

y:=y+d*t;

l0:=CONCAT(l0,{m});

l1:=CONCAT(l1,{d});

l2:=CONCAT(l2,{y});  

END;

l3:=CONCAT(l0,l1);

l4:=CONCAT(l3,l2);

m0:=list2mat(l4,SIZE(l0));

m0:=TRN(m0);

RETURN m0;

 

END;

The result is a matrix wit the columns:

Column 1:  time  (t = m)

Column 2:  velocity  (dy/dt = d)

Column 3:  position (y)

The program assumes that the object or person being dropped is well above the ground or floor.  

Example

Go 10 steps with Δ = 0.25 sec, g = 9.80665 m/s^2, and α = 0.028

Velocity ≈ 18.6716 m/s

Position ≈ 76.1314 m

The program assumes that the object or person being dropped is well above the ground or floor.  

Source

Eisberg, Robert M.  Applied Mathematical Physics with Programmable Pocket Calculators  McGraw-Hill Book Company:  New York  1976.   ISBN 0-07-019109-3

I want to wish you a Happy New Year. May you have a healthy, prosperous, and happy 2023!

Note:  For January and February 2023, my posting schedule will be on Saturdays only, starting January 7.  This doesn't include any firmware updates or reviews, they will be on Mondays should they occur.    One of my resolutions for 2023 is to catch up on my reading of math books and articles.

Eddie 

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP 75C Program Collection

HP 75C Program Collection

Merry Christmas everyone!   I hope everyone is safe, happy, and blessed.

LAWCOS:  Law of Cosines

335 bytes

100 DISP "Law of Cosines" @ WAIT .25

105 OPTION ANGLE DEGREES

180 DISP "Θ is opp. side a" @ WAIT .25

110 INPUT "1) Side, 2) Angle? "; H

115 ON H GOTO 1000, 2000

1000 INPUT "b?, c?, Θ? "; B,C,T

1010 A=SQR(B^2+C^2-2*B*C*COS(T))

1020 DISP "a: "; STR$(A) @ END

2000 INPUT "a?, b?, c? "; A,B,C

2010 T=ACOS((B^2+C^2-A^2)/(2*B*C))

2020 DISP "Θ:"; STR$(T); "°" @ END

Example:

1) Side:  1

B = 11.78, C = 32.12, T = 60

Result:  a = 28.1440793063

2)  Angle: 2

A = 14.55, B = 12.65, C = 17.00

Result:  Θ = 56.5108780171°

SPECPOLY:  Special Polynomials

526 bytes  (10/27/2022)

1.Cheb:  Chebyshev Polynomial of the 1st order

2.Herm:  Hermite Polynomial 

3.Lagur:  Laguerre Polynomial (with α=0)

4.Legen:  Legendre Polynomial of the 1st Order

100 DISP "Polynomials:  Type?" @ WAIT .5

105 INPUT "1.Cheb 2.Herm 3.Lagur 4.Legen:"; H

110 INPUT "x? "; X

115 INPUT "order? ";N

120 A=1 @ B=X*(H=1 OR H=4)+2*X*(H=2)+(1-X)*(H=3)

300 IF N=0 THEN DISP A @ END

302 IF N=1 THEN DISP B @ END

305 FOR I=2 TO N

310 ON H GOSUB 500,505,510,515

315 A=B

320 B=C

325 NEXT I

330 DISP C

335 END

500 C=2*X*B-A @ RETURN

505 C=2*X*B-2*(I-1)*A @ RETURN

510 C=((2*(I-1)+1-X)*B-(I-1)*A)/I @ RETURN

515 C=((2*I-1)*X*B-(I-1)*A)/I @ RETURN

Source:

Davidson, James J.  "Chebyshev Polynomials, First & Second Kind, Tn(x) & Un(x)", "Hermite Polynomials, H(n); n≥n", "Laguerre Polynomials, Generalized, Ln^(α)(x)", "Legendre Functions, First & Second Kinds, Pn(x) & Qn(x)"  ENTER 65 NOTES  Vol. 3 No. 8 September 1976  pp. 11-12

Examples:

x = 11, order = 6

1.  Cheb:  55989361

2.  Herm: 106439224

3.  Lagur: -35.5902777778

4.  Legen: 25289461

ENGINE:  Automotive Engine Mathematics

630 bytes (10/27/2022)

100 DISP "Engine Math" @ WAIT .5

110 INPUT "# cylinders? "; N

120 DISP "Solve for?" @ WAIT .25

125 INPUT "1)DSP, 2)STROKE, 3)BORE "; H

130 IF H#1 THEN INPUT "DSP? "; D

135 IF H#2 THEN INPUT "STROKE? "; S

140 IF H#3 THEN INPUT "BORE? "; B

145 IF H=1 THEN LET D=PI/4*B^2*S*N

150 IF H=2 THEN LET S=D/(PI/4*B^2*N)

155 IF H=3 THEN LET B=SQR(D/(PI/4*S*N))

160 DISP "DPS= "; D @ STOP

165 DISP "STORKE= "; S @ STOP

170 DISP "BORE= "; B @ STOP

205 INPUT "RPM? (y/n) "; I$

210 IF UPRC(I$)="N" THEN 400

300 INPUT "RPM? "; R

310 P=S*R/6

320 E=R*D*.85/3456

350 DISP "Piston Speed="; P @ STOP

360 DISP "St. Carb CFM= "; E @ STOP

370 INPUT "Again? (y/n) "; I$ 

375 IF UPRC(I$)="Y" THEN 300

400 DISP "Done."

Source:

Lawlor, John.  Auto Math Handbook.  Calculations, Formulas, Equations, and Theory for Automotive Enthusiasts.  HP Books:  Berkeley Publishing Group:  New York, NY.  1991.  ISBN 1-55788-020-4

LINREG:  Linear Regression

568 bytes (10/31/2022)

100 DISP "y=mx+b" @ WAIT .5

110 S0=0 @ S1=0 @ S2=0 @ S3=0 @ S4=0 @ S5=0

120 DISP 'Σ+ Σ- Calc'

130 K$=KEY$ @ IF K$='' THEN 130

140 IF K$="+" THEN H=1 @ GOTO 200

150 IF K$="-" THEN H=-1 @ GOTO 200

160 IF UPRC$(K$)='C' THEN 400

170 GOTO 130

200 INPUT 'x,y? '; X,Y

210 S0=S0+H @ S1=S1+H*X @ S2=S2+H*Y

220 S3=S3+H*X^2 @ S4=S4+H*Y^2 @ S5=S5+H*X*Y

230 DISP S0 @ WAIT .5 @ GOTO 120

400 B=(S5-S1*S2/S0)/(S3-S1^2/S0)

440 A=(S2-B*S1)/S0

450 R=B*SQR((S0*S3-S1^2)/(S0*S4-S2^2))

470 DISP 'type cont...' @ WAIT .5

500 DISP 'SLP=';B @ STOP

510 DISP 'ITC=';A @ STOP

520 DISP 'CORR=';R

Instructions:

Press + to add data.  Separate  x and y with a comma.

Press - to delete data.  Separate x and y with a comma.

Press C to determine the slope, intercept, and correlation.

Example:

Data:

5, 4.066

8, 4.125

11, 4.202

18, 4.293

21, 4.349

ITC ≈ 3.99046

SLP ≈ 0.01719

CORR ≈ 0.99376

Source:

Hewlett Packard.  HP 12C User Guide  Edition 4.  San Diego, CA  2004.

SIMPSON:  Integral Using Simpson’s Rule Approximation

size varies - around 300 bytes

∫ FNF(X) dX from X = a to X = b

Line 100 is where you have to define your function (of X). 

100 DEF FNF(X) = [define f(x) here]

115 OPTION ANGLE RADIANS

120 INPUT "a? ";A

125 INPUT "b? ";B

130 INPUT "# parts (even)? ";N

135 T=FNF(A)+FNF(B)

140 H=(B-A)/N

145 FOR I TO N-1

150 IF FP(I/2)=0 THEN 155 ELSE 160

155 T=T+2*FNF(A+I*H) @ GOTO 165

160 T=T+4*FNF(A+I*H)

165 NEXT I

170 T=T*H/3

175 DISP "Integral = ";T

Examples:

For both examples, n = 24

FNF(X)= 2*X^2+3,  a = 1, b = 6, result:  158.333333333

FNF(X)=2*COS(X), a = 0, b = .785398163398, result:  1.41421357139  (exact √2)

Happy Holidays everyone!

Next post will be on New Years' Eve:  December 31, 2022.

Eddie 

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Retro Review: HP 75C

Retro Review:  HP 75C

It's Christmas Eve!

Quick Facts

Model:  HP 75C 

Company:  Hewlett Packard

Years:  1982-1984

Type:  Scientific, BASIC Programmable

Batteries: Rechargeable Ni-CAD, with AC-Adapter**

Display:  1 line, 32 characters

Original Price:  $995

Memory:  16,000 bytes RAM with a slot for an 8K RAM Card

Other Ports:  3 ROM slots for applications 

Hard Case which stores the HP 75 and the cards, but not the AC adapter

The HP 75C (and later HP 75D) has an 8-bit CPU microprocessor named the Capricorn.   The Capricorn microprocessors where featured in the HP 85 computer.

For fans of tropical astrology, this article is posted on December 24, under the sign of Capricorn.   ♑  The Capricorn processor was designed by a Steve Wozniak, a Leo.  But I digress.

Introduction

The HP 75C computer is a portable computer with an almost full sized QWERTY keyboard.  The 75C is a scrolling one-line display that can have up to 32 characters.  The keyboard works like a computer keyboard: the [SHIFT] key must be pressed and held to type capital letters.

The keyboard is nice to type and with the correct size of hands, touch typing can be accomplished.  It also has a numeric keypad that can be activated by holding down [CTL] while pressing [LOCK].   Pressing [LOCK] ends the numeric keypad mode.

[ 7 ]  returns 7

[ 8 ]  returns 8

[ 9 ]  returns 9

[ U ] returns 4

[ I ] returns 5

[ O ] returns 6

[ J ] returns 1

[ K ] returns 2

[ L ] returns 3

[ M ] returns 0

Other characters can be accessed by holding down the [CTL] key and pressing another key.   Example characters that can be typed this way are:

CTL + Space:  Δ

CTL + A:  °

CTL + D:  α

CTL + I:  σ

CTL + P:  θ

CTL + T:  π

CTL + plus key:  Σ

The keyboard also has an HP-IL port and a card reader.  The card reader is manual, requiring the user to pull the card at just the right speed to record programs.  Transferring programs to cards, which are long and skinny, takes a lot of patience.  Each card be pulled in two ways and each way can store a program up to only 650 bytes.   Every time a new program is stored in a track, that new program replaces the previous contents.     

The battery is a rechargeable Ni-CAD battery.  If you purchase a HP 75C, I advise you to get one with a working AC plug.  According to the HP 75 Owner's Manual, it takes about 8 hours for the batteries to fully recharge.  

See the Sources section for a download link to the Owner's Manual.  

How to turn the HP 75C on?   There is no ON key.   The [ATTN] (attention) key takes care of this.  To turn the 75C off, hold [SHIFT] and press [ATTN] or type bye then [RTN]. 

Modes

The HP 75C has three operating modes:

TIME: setting the computer's clock and time.  Thankfully the HP 75C is Y2K friendly and allows dates after 2000.

APPT:  set and check personal appointments.

EDIT:  the main mode of the HP 75C computer.  This is where all the basic programs are edited, stored, and ran.   The Edit mode can handle one line algebraic calculations, with the order of operations followed.  

Programming

The HP 75C has BASIC programming language, although not as extensive as the HP 71B.  It's probably the one slight problem I have with the 75C, but missing functions can be programmed.   In tomorrow's post, I have a simple linear regression which the 75C's list of commands lack commands for.

What is included?  A short list includes:

*  square roots, modulus, sign, maximum, minimum, random numbers, remainder, integer part, fractional part 

*  the constants PI, INF (9.99999999999E499), EPS (1E-499)

*  degree/radian angle conversions, trigonometric functions, angle (atan2), sec, sec, cot, logarithms (log10 and log (for ln, this is a computer language))

*  relational tests (evaluated to 0 for false or 1 for true), logic (and, or, exor (either or but not both), not)

*  strings, alarm settings, beep, read and data, goto and label, for-to-step structure, if-then-else structure, character, date and time strings, arrays

*  printing and user function commands

Remember, in programming the 75C, line numbers are required.   

Like the HP 71B, I find it a joy to program the 75C.  

The Updated HP 75D

The HP 75D was an updated HP 75C computer and produced in rare supply from 1984 to 1986.  The retail price of an HP 75D was $1,095 and included a port for a  bar code wand. Yes, the same type of bar codes that you see on grocery products and you scan at the self checkout lines.   

Final Thoughts 

The HP 75C is not an inexpensive purchase.  If you buy one, please be sure you see pictures from the seller with the unit turned on.  In addition, at the very least, make sure it has working batteries and the AC adapter.   The going price for the HP 75C these days from at least $250 US.   

It is a worthwhile machine especially for fans of BASIC and a good companion to the HP 71B.   I am happy to have the 75C in my collection, which is years I missed out on winning one as a door prize.  

Sources

"HP-75"  Wikipedia.  September 7, 2021.   Retrieved December 4, 2022.  https://en.wikipedia.org/wiki/HP-75

"HP-75C/D"  Museum of HP Calculators.   Retrieved December 4, 2022.

https://www.hpmuseum.org/hp75.htm

Hewlett Packard.  HP-75 Owner's Manual.  Rev. B   November 1982.  

Download from the hpcalc.org's literature page here:  https://literature.hpcalc.org/items/1072

Until next time, keep happy and sane,

Eddie 

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.